REGENERATION IN MARKOV-CHAIN SAMPLERS

Markov chain sampling has recently received considerable attention, in particular in the context of Bayesian computation and maximum likelih ood estimation. This article discusses the use of Markov chain splitti ng, originally developed for the theoretical analysis of general state -space Markov chains, to introduce regeneration into Markov chain samp lers. This allows the use of regenerative methods for analyzing the ou tput of these samplers and can provide a useful diagnostic of sampler performance. The approach is applied to several samplers, including ce rtain Metropolis samplers that can be used on their own or in hybrid s amplers, and is illustrated in several examples.